From 8a429a6044b4f030235ffab2ea621caba68b8f71 Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Thu, 23 Jan 2014 09:59:33 +0100 Subject: [PATCH] TikZ'en eines Bildes und Bemerkungen --- documents/GeoTopo/Arbeitszeit.md | 1 + documents/GeoTopo/GeoTopo.pdf | Bin 4914771 -> 4916450 bytes documents/GeoTopo/Kapitel4.tex | 6 +-- documents/GeoTopo/Vorwort.tex | 4 +- documents/GeoTopo/figures/triangle-3.tex | 39 +++++++++++++++++++ tikz/triangle-3/Makefile | 31 +++++++++++++++ tikz/triangle-3/Readme.md | 3 ++ tikz/triangle-3/triangle-3.png | Bin 0 -> 34493 bytes tikz/triangle-3/triangle-3.tex | 47 +++++++++++++++++++++++ 9 files changed, 126 insertions(+), 5 deletions(-) create mode 100644 documents/GeoTopo/figures/triangle-3.tex create mode 100644 tikz/triangle-3/Makefile create mode 100644 tikz/triangle-3/Readme.md create mode 100644 tikz/triangle-3/triangle-3.png create mode 100644 tikz/triangle-3/triangle-3.tex diff --git a/documents/GeoTopo/Arbeitszeit.md 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f4a96b6..9baf0f6 100644 --- a/documents/GeoTopo/Kapitel4.tex +++ b/documents/GeoTopo/Kapitel4.tex @@ -649,8 +649,8 @@ Der Flächeninhalt eines Dreiecks ist $\nicefrac{1}{2} \cdot \text{Grundseite} \ \begin{figure} \centering - \input{figures/todo.tex} - \caption{Flächenberechnung im Dreiecks (Bild 7)} + \input{figures/triangle-3.tex} + \caption{$\triangle ABL_a$ und $\triangle C{L_C}B$ sind ähnlich, weil $\IWS = \pi$} \label{fig:flaechenberechnung-dreieck-2} \end{figure} @@ -684,7 +684,7 @@ $\overset{\text{Strahlensatz}}{\Rightarrow} \frac{a}{h_c} = \frac{c}{h_a} \right $X=\mdr^2$, $d = \text{euklidischer Abstand}$, $G = \text{Menge der üblichen Geraden}$. \end{satz} -\begin{beweis} +\begin{beweis}\leavevmode \begin{enumerate}[label=(\roman*)] \item $(\mdr^2, d_\text{Euklid})$ ist offensichtlich eine euklidische Ebene. \item Sei $(X,d)$ eine euklidische Ebene und $g_1, g_2$ Geraden diff --git a/documents/GeoTopo/Vorwort.tex b/documents/GeoTopo/Vorwort.tex index 49f0627..5c5354b 100644 --- a/documents/GeoTopo/Vorwort.tex +++ b/documents/GeoTopo/Vorwort.tex @@ -10,8 +10,8 @@ Die Kurz-URL des Projekts lautet \href{http://tinyurl.com/GeoTopo}{tinyurl.com/G An dieser Stelle möchte ich noch Herrn Prof. Dr. Herrlich für einige Korrekturvorschläge und einen gut strukturierten Tafelanschrieb danken, der als Vorlage für dieses Skript diente. -Vielen Dank auch an Frau Lenz, die es mir erlaubt hat, ihre -Übungsaufgaben und Lösungen zu benutzen. +Vielen Dank auch an Frau Lenz und Frau Randecker, die es mir erlaubt +haben, ihre Übungsaufgaben und Lösungen zu benutzen. \textbf{Was ist Topologie?} diff --git a/documents/GeoTopo/figures/triangle-3.tex b/documents/GeoTopo/figures/triangle-3.tex new file mode 100644 index 0000000..ef3b4f0 --- /dev/null +++ b/documents/GeoTopo/figures/triangle-3.tex @@ -0,0 +1,39 @@ +\begin{tikzpicture} + \tkzSetUpPoint[shape=circle,size=10,color=black,fill=black] + \tkzSetUpLine[line width=1] + \tkzDefPoints{0/0/A, 4/0/B, 3/3/C} + + \tkzDefLine[orthogonal=through A,/tikz/overlay](B,C) \tkzGetPoint{helper} + \tkzInterLL(B,C)(A,helper) \tkzGetPoint{La} + \tkzDefLine[orthogonal=through C,/tikz/overlay](A,B) \tkzGetPoint{helper} + \tkzInterLL(A,B)(C,helper) \tkzGetPoint{Lc} + + \tkzInterLL(A,La)(C,Lc) \tkzGetPoint{orthocenter} + + \tkzMarkAngle[arc=l,size=1.0cm,color=red,fill=red!20](B,A,La) + \tkzLabelAngle[pos=0.8](B,A,La){$\alpha$} + + \tkzMarkAngle[arc=l,size=1.0cm,color=red,fill=red!20](Lc,C,B) + \tkzLabelAngle[pos=0.8](Lc,C,B){$\alpha$} + + \tkzMarkAngle[arc=ll,size=0.6cm,color=green,fill=green!20](A,orthocenter,Lc) + \tkzLabelAngle[pos=0.4](A,orthocenter,Lc){$\gamma$} + + \tkzMarkAngle[arc=ll,size=0.4cm,color=green,fill=green!20](La,orthocenter,C) + \tkzLabelAngle[pos=0.2](La,orthocenter,C){$\gamma$} + + \tkzDrawPolygon(A,B,C) + + \node at ($(A)+(-0.47,-0.2)$){$A$}; + \node at ($(B)+(0.35,-0.2)$) {$B$}; % \tkzLabelPoint[below](B){$B$} is not accurate enough + \node at ($(C)+(0.05,0.3)$) {$C$}; + \node at ($(La)+(0.25,0.1)$) {$L_A$}; + \node at ($(Lc)+(0,-0.25)$) {$L_C$}; + + \tkzDrawSegment(C,Lc) + \tkzDrawSegments(A,La) + \tkzDrawPolygon[pattern=north east lines](A,B,La) + \tkzDrawPolygon[pattern=north west lines](Lc,B,C) + \tkzDrawPoints(A,B,C,La,Lc) + %\tkzLabelSegment[pos=0.7,below](A,B){$c$} +\end{tikzpicture} diff --git a/tikz/triangle-3/Makefile b/tikz/triangle-3/Makefile new file mode 100644 index 0000000..65ddf30 --- /dev/null +++ b/tikz/triangle-3/Makefile @@ -0,0 +1,31 @@ +SOURCE = triangle-3 +DELAY = 80 +DENSITY = 300 +WIDTH = 512 + +make: + pdflatex $(SOURCE).tex -output-format=pdf + make clean + +clean: + rm -rf $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot + +gif: + pdfcrop $(SOURCE).pdf + convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif + make clean + +png: + make + make svg + inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png + +transparentGif: + convert $(SOURCE).pdf -transparent white result.gif + make clean + +svg: + #inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg + pdf2svg $(SOURCE).pdf $(SOURCE).svg + # Necessary, as pdf2svg does not always create valid svgs: + inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg diff --git a/tikz/triangle-3/Readme.md b/tikz/triangle-3/Readme.md new file mode 100644 index 0000000..a9abd03 --- /dev/null +++ b/tikz/triangle-3/Readme.md @@ -0,0 +1,3 @@ +Compiled example +---------------- +![Example](triangle-3.png) diff --git a/tikz/triangle-3/triangle-3.png b/tikz/triangle-3/triangle-3.png new file mode 100644 index 0000000000000000000000000000000000000000..bcd34fa1a702176077eea310b623ef6046a2729a GIT binary patch literal 34493 zcmcG#c|4Tw7e72R#xiz>>|{@}4B4`biX>YlvQtwb`@Uwzl1xTYpDbBZ5@o9_S*I|R zwX&3T3?ae{VlZZ&d;0!<&tK2KkJrm<<{s|rzRo%CbI$vma}D;QtpyLKI41}M;;}q$ zb{PbM0B^x*9BjagUYOH2-~}3X#_|dW@DtB*BMrEQ1)p~g1A!DCF@M2_oXtJJhhpL8 zPT}@Jx5A^Yh28{3MMbIm2Kt4et_9yz4+{0pUpEp5fsTSK%}!s5F8EUzRUl-(Pw1#m 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+\begin{tikzpicture} + \tkzSetUpPoint[shape=circle,size=10,color=black,fill=black] + \tkzSetUpLine[line width=1] + \tkzDefPoints{0/0/A, 4/0/B, 3/3/C} + + \tkzDefLine[orthogonal=through A,/tikz/overlay](B,C) \tkzGetPoint{helper} + \tkzInterLL(B,C)(A,helper) \tkzGetPoint{La} + \tkzDefLine[orthogonal=through C,/tikz/overlay](A,B) \tkzGetPoint{helper} + \tkzInterLL(A,B)(C,helper) \tkzGetPoint{Lc} + + \tkzInterLL(A,La)(C,Lc) \tkzGetPoint{orthocenter} + + \tkzMarkAngle[arc=l,size=1.0cm,color=red,fill=red!20](B,A,La) + \tkzLabelAngle[pos=0.8](B,A,La){$\alpha$} + + \tkzMarkAngle[arc=l,size=1.0cm,color=red,fill=red!20](Lc,C,B) + \tkzLabelAngle[pos=0.8](Lc,C,B){$\alpha$} + + \tkzMarkAngle[arc=ll,size=0.6cm,color=green,fill=green!20](A,orthocenter,Lc) + \tkzLabelAngle[pos=0.4](A,orthocenter,Lc){$\gamma$} + + \tkzMarkAngle[arc=ll,size=0.4cm,color=green,fill=green!20](La,orthocenter,C) + \tkzLabelAngle[pos=0.2](La,orthocenter,C){$\gamma$} + + \tkzDrawPolygon(A,B,C) + + \node at ($(A)+(-0.47,-0.2)$){$A$}; + \node at ($(B)+(0.35,-0.2)$) {$B$}; % \tkzLabelPoint[below](B){$B$} is not accurate enough + \node at ($(C)+(0.05,0.3)$) {$C$}; + \node at ($(La)+(0.25,0.1)$) {$L_A$}; + \node at ($(Lc)+(0,-0.25)$) {$L_C$}; + + \tkzDrawSegment(C,Lc) + \tkzDrawSegments(A,La) + \tkzDrawPolygon[pattern=north east lines](A,B,La) + \tkzDrawPolygon[pattern=north west lines](Lc,B,C) + \tkzDrawPoints(A,B,C,La,Lc) + %\tkzLabelSegment[pos=0.7,below](A,B){$c$} +\end{tikzpicture} +\end{document}

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